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Poisson's Equation

mattferraro.dev

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Re: Poisson's Equation

#101

Post by MontyCarloHall »

sdenton4 wrote: post #88
lordnacho wrote: post #63

Earlier quoted context omitted.

I feel the same. How can it be that I went to a world famous institution providing 2-to-1 student-teacher ratios, but I still think the best explanations are these modern internet explanations? I guess the best explanations just bubble up in the modern environment. > you're not supposed to learn everything in college, you're supposed to learn how to learn But to learn how to learn, you gotta learn some things to a so…

Interesting to think a bit about student/teacher ratios (STR). The up-side is that with a low STR (2:1), the teacher can adapt to the particular strengths and weaknesses of the students, to get the best reinforcement. The /downside/ is that the students will typically also have fewer teachers overall, and are maybe stuck with a bad one. (This is the problem of bad grad school advisors in a nutshell...) In this world,…

The latter regime is less a function of the ratio itself and more a function of the total number of accessible teachers, and the ability to switch teachers at will to find the one most suited to your learning style. If a university had 100 teachers all teaching the same course in the low or medium STR regimes and students were able to easily swap between teachers at will, the effect would be the same.

Re: Poisson's Equation

#102

Post by p_j_w »

SavantIdiot wrote: post #56

I could have used this 32(!) years ago when I was struggling in college. (This and 3b1b.) It amazes me just how many key topics were so inaccessible to the majority of the class at engineering school. I base this on observations from group study sessions and the hyper-aggressive test curves. I knew lots of people who never got the hang of div/grad/curl, or a Jacobians, or eignenvectors, or Z-transforms... These are k…

>I could have used this 32(!) years ago when I was struggling in college.

I was struggling with this material more like 15 years ago, but same. I wish someone had explained the LaPlacian like this when I was in Multivariable calculus:

>Find me a function f where every value everywhere is the average of the values around it.

It's so simple and easy to grasp, yet provides so much insight into what's going on when you're doing the actual calculation behind the operation, but is so easy to lose sight of when you're overwhelmed with figuring out the 'mechanics' of it and everything else that was covered in the day's lesson plan.

Re: Poisson's Equation

#103

Post by lordnacho »

mensetmanusman wrote: post #89
lordnacho wrote: post #63

Earlier quoted context omitted.

I feel the same. How can it be that I went to a world famous institution providing 2-to-1 student-teacher ratios, but I still think the best explanations are these modern internet explanations? I guess the best explanations just bubble up in the modern environment. > you're not supposed to learn everything in college, you're supposed to learn how to learn But to learn how to learn, you gotta learn some things to a so…

The answer is statistics: what is more likely, that the best explainer of a certain topic is within a group of people you have access to, or that person is somewhere else in the world? This is very analogous to the problem industrial research groups face trying to answer a certain problem, e.g. ‘how do we ensure that our team is the most likely to solve a particular problem first?’ This is why start up acquisitions a…

Might also have something to do with the explanation size: this Poisson thing is one little thing. With the internet, it's perfectly acceptable to just do a blog post on one little thing.

Previously, if you were to write a textbook or teach a tutorial, you needed to teach a bunch of things.

So in the internet age there's a bunch of fine grained "best explanations" coming from a variety of authors that beats the best that one guy can do across a range of topics.

Re: Poisson's Equation

#104

Post by lordnacho »

pfortuny wrote: post #69
lordnacho wrote: post #63

Earlier quoted context omitted.

I feel the same. How can it be that I went to a world famous institution providing 2-to-1 student-teacher ratios, but I still think the best explanations are these modern internet explanations? I guess the best explanations just bubble up in the modern environment. > you're not supposed to learn everything in college, you're supposed to learn how to learn But to learn how to learn, you gotta learn some things to a so…

Honest question. 2-to-1 student-teacher ratio?? Where is that? Totally stunned.

Oxford, and the place out in the marshes.

It's not that there aren't massive lectures, tutorials are in addition to those.

Not bad value actually, despite what I said earlier. You do get to ask about whatever your mental block is, and the tutor is gonna know. But studying is time consuming, an hour is not as much time as it seems. You probably learn the most on your own, which nowadays ought to mean on the internet.

Re: Poisson's Equation

#105

Post by sdenton4 »

MontyCarloHall wrote: post #101
sdenton4 wrote: post #88

Earlier quoted context omitted.

Interesting to think a bit about student/teacher ratios (STR). The up-side is that with a low STR (2:1), the teacher can adapt to the particular strengths and weaknesses of the students, to get the best reinforcement. The /downside/ is that the students will typically also have fewer teachers overall, and are maybe stuck with a bad one. (This is the problem of bad grad school advisors in a nutshell...) In this world,…

The latter regime is less a function of the ratio itself and more a function of the total number of accessible teachers, and the ability to switch teachers at will to find the one most suited to your learning style. If a university had 100 teachers all teaching the same course in the low or medium STR regimes and students were able to easily swap between teachers at will, the effect would be the same.

The ratio is really what matters more than absolute numbers; it tells us where the bottleneck is (supply or demand).

If the STR is 2:1 and you've got 1000 teachers, it means you've got 2000 students. If only 5% of teachers are good (see: sturgeon's law), you've still got competition centered on the student side, as 2k students fight to get into the classes with the 50 good teachers.

Re: Poisson's Equation

#106

Post by mywittyname »

sdenton4 wrote: post #88
lordnacho wrote: post #63

Earlier quoted context omitted.

I feel the same. How can it be that I went to a world famous institution providing 2-to-1 student-teacher ratios, but I still think the best explanations are these modern internet explanations? I guess the best explanations just bubble up in the modern environment. > you're not supposed to learn everything in college, you're supposed to learn how to learn But to learn how to learn, you gotta learn some things to a so…

Interesting to think a bit about student/teacher ratios (STR). The up-side is that with a low STR (2:1), the teacher can adapt to the particular strengths and weaknesses of the students, to get the best reinforcement. The /downside/ is that the students will typically also have fewer teachers overall, and are maybe stuck with a bad one. (This is the problem of bad grad school advisors in a nutshell...) In this world,…

> which /maybe/ causes student quality to drop.

Not maybe. Absolutely. Even paid-for online courses have a relatively high drop out rate.

But that's okay. It's the price to pay to achieve the volume needed to pay for great instruction. I can take a music theory class from an instructor who would never waste their time teaching someone like me. Even though I may not get much more than entertainment value from it. I'm effectively subsidizing the students who do learn something concrete from the course.

There might be an argument to be made that pandering to an "edutainment" crowd might reduce the quality of instruction, but a good instructor should be able to find the right balance.

Re: Poisson's Equation

#107

Post by wheelinsupial »

SubiculumCode wrote: post #77
RicoElectrico wrote: post #16

Earlier quoted context omitted.

I'd rather have more submissions like this on the HN frontpage than the slew of entrepreneurship advice (good or bad), programming-languages-du-jour and disguised content marketing. Anyway, the premise that "everything I see has to appeal to me" would best stay on YouTube where it originated.

It IS a good article, but the audience of the article is fairly specific yet left unspecified. As a general principal in technical writing it is advisable to start with a "why you should care" statement because this naturally informs the reader about the context.

Is the second section “when would I use this” sufficient to provide a “why you should care statement”? Or is there a more common way to call this out in technical writing? Perhaps an “intended audience” or “necessary prerequisites”?

Re: Poisson's Equation

#108

Post by pfortuny »

lordnacho wrote: post #104
pfortuny wrote: post #69

Earlier quoted context omitted.

Honest question. 2-to-1 student-teacher ratio?? Where is that? Totally stunned.

Oxford, and the place out in the marshes. It's not that there aren't massive lectures, tutorials are in addition to those. Not bad value actually, despite what I said earlier. You do get to ask about whatever your mental block is, and the tutor is gonna know. But studying is time consuming, an hour is not as much time as it seems. You probably learn the most on your own, which nowadays ought to mean on the internet.

Oh I thought it was accross the pond. I knew about Oxford etc. but for whatever reason I took it to be in the Colonies.

Re: Poisson's Equation

#109

Post by nimish »

lordnacho wrote: post #63
SavantIdiot wrote: post #56

I could have used this 32(!) years ago when I was struggling in college. (This and 3b1b.) It amazes me just how many key topics were so inaccessible to the majority of the class at engineering school. I base this on observations from group study sessions and the hyper-aggressive test curves. I knew lots of people who never got the hang of div/grad/curl, or a Jacobians, or eignenvectors, or Z-transforms... These are k…

I feel the same. How can it be that I went to a world famous institution providing 2-to-1 student-teacher ratios, but I still think the best explanations are these modern internet explanations? I guess the best explanations just bubble up in the modern environment. > you're not supposed to learn everything in college, you're supposed to learn how to learn But to learn how to learn, you gotta learn some things to a so…

Turns out that mathematics pedagogy is poor, in general. Especially for geometry and vector calculus, where it's either obsolete, busted systems or incredibly abstruse ones.

Skipping over div/grad/curl and Gibbs-Heaviside vector calculus by going straight to differential forms and Clifford algebras (geometric calc) would save a bunch of heartache and pointless effort.

Linear algebra is essential since the whole point of differentiation is to construct linear approximations of functions...among other things.

Re: Poisson's Equation

#110

Post by MontyCarloHall »

sdenton4 wrote: post #105
MontyCarloHall wrote: post #101

Earlier quoted context omitted.

The latter regime is less a function of the ratio itself and more a function of the total number of accessible teachers, and the ability to switch teachers at will to find the one most suited to your learning style. If a university had 100 teachers all teaching the same course in the low or medium STR regimes and students were able to easily swap between teachers at will, the effect would be the same.

The ratio is really what matters more than absolute numbers; it tells us where the bottleneck is (supply or demand). If the STR is 2:1 and you've got 1000 teachers, it means you've got 2000 students. If only 5% of teachers are good (see: sturgeon's law), you've still got competition centered on the student side, as 2k students fight to get into the classes with the 50 good teachers.

Ah, I get your point now. In my hypothetical example, you could still have those 2000 students enrolled with only the 50 good teachers. The overall STR would still be 2:1, but most of the teachers would have no students, so the effective STR would be 40:1.

The main thing distinguishing online education is the ability for students to all flock to the good teachers and completely abandon the crappy ones.

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